Give exact solutions for 3secx - cosx = 2, where x is greater or equal to zero and less than or equal to 2pi. ?

1 Answer
Jim G.
Apr 18, 2018

#x=0,x=2pi#

Explanation:

#"using the "color(blue)"trigonometric identity"#

#•color(white)(x)secx=1/cosx#

#rArr3/cosx-cosx=2#

#"multiply through by "cosx#

#rArr3-cos^2x=2cosx#

#"this is a quadratic in cos"#

#"rearranging in "color(blue)"standard form"#

#cos^2x+2cosx-3=0larrcolor(blue)"in standard form"#

#"the factors of - 3 which sum to + 2 are + 3 and - 1"#

#rArr(cosx+3)(cosx-1)=0#

#"equate each factor to zero and solve for x"#

#cosx+3=0rArrcosx=-3" is invalid since"#

#-1<=cosx<=1#

#cosx-1=0rArrcosx=1rArrx=0,2pi#

#"solutions are "x=0" or "x=2pito(0<=x<=2pi)#

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